I've cut and pasted the following from NCSU. Bacterial Speck and Spot would be treated the same. Section F below is for field sprays.

Moncozeb PLUS copper is recommended, as you can see. Mancozeb alone contains zinc and manganese. Kocide or any other copper containing prep might also be useful.

Trying to control the bacterial folaige diseases is not easy at all, unfortunately.

E. Prevent bacterial leafspot in the plant beds:

keep the greenhouse as dry as possible and avoid splashing water;
spray with a fixed copper (Tribasic Copper Sulfate 4 lb, Copper-Count N, or Citcop 4E 2 to 3 qt, or Kocide 101 1.0 to 1.5 lb per 100 gal water). The addition of 200 ppm streptomycin (Agri-mycin 17-1.0 lb in 100 gal of the copper spray with a spreader-sticker) will improve the effectiveness of the spray program. Make applications on a 7- to 10-day schedule if spots appear, and one day before pulling plants.
F. In the field start spray schedule when the disease first appears. However, do not use streptomycin in the field.

Mix fixed copper (see E above for amount) and 1.5 lbs of mancozeb (Manzate 200DF or Dithane M-45) or maneb (Maneb 80WP, Maneb 75DF, Manex) in 100 gal of water. Do not use mancozeb on tomatoes within 5 days of harvest. Mancozeb is not registered for use on peppers; use maneb.
Adjust sprayer and speed of tractor to obtain complete coverage of all plant surfaces. Spray pressure of 200-400 psi is recommended and the use of at least three nozzles per row for pepper and 5 drop nozzles per row for tomato. Depending on plant size, use 50-150 gal/A of finished spray.
Adjust spray schedules according to the weather and presence of disease:
(a) Spray one week after plants are set; (b) spray every 5 to 7 days during rainy periods; spray on 10-day intervals during drier weather; (c) spray before rain is forecast but allow time for spray to dry.

Carolyn